```html
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    <title>异或运算：找出唯一出现的元素</title>
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<body class="antialiased">
    <!-- Hero Section -->
    <section class="hero text-white py-20 px-4 md:px-0">
        <div class="container mx-auto max-w-5xl text-center">
            <h1 class="text-4xl md:text-5xl font-bold mb-6 font-serif">异或运算的巧妙应用</h1>
            <p class="text-xl md:text-2xl mb-8 max-w-3xl mx-auto leading-relaxed">
                探索如何用<span class="font-bold text-yellow-200">O(n)时间</span>和<span class="font-bold text-yellow-200">O(1)空间</span>复杂度找出数组中唯一出现的元素
            </p>
            <div class="flex justify-center space-x-4">
                <a href="#concept" class="px-6 py-3 bg-white text-indigo-600 font-semibold rounded-full hover:bg-gray-100 transition duration-300">
                    <i class="fas fa-lightbulb mr-2"></i>核心原理
                </a>
                <a href="#solution" class="px-6 py-3 bg-indigo-700 text-white font-semibold rounded-full hover:bg-indigo-800 transition duration-300">
                    <i class="fas fa-code mr-2"></i>代码实现
                </a>
            </div>
        </div>
    </section>

    <!-- Main Content -->
    <main class="container mx-auto max-w-5xl px-4 py-12">
        <!-- Problem Intro -->
        <section class="mb-16">
            <div class="bg-white rounded-xl shadow-md overflow-hidden p-8">
                <h2 class="text-3xl font-bold text-gray-800 mb-6 font-serif">问题描述</h2>
                <p class="text-lg text-gray-700 mb-6 leading-relaxed">
                    给定一个整数数组，其中<span class="font-bold text-indigo-600">所有元素都成对出现</span>，<span class="font-bold text-indigo-600">只有一个元素是唯一的</span>。如何高效地找出这个唯一的元素？
                </p>
                <div class="flex flex-wrap -mx-4">
                    <div class="w-full md:w-1/2 px-4 mb-6 md:mb-0">
                        <div class="bg-blue-50 p-6 rounded-lg h-full">
                            <h3 class="text-xl font-semibold text-gray-800 mb-3 flex items-center">
                                <i class="fas fa-exclamation-circle text-blue-500 mr-2"></i>传统解法
                            </h3>
                            <ul class="text-gray-700 space-y-2">
                                <li class="flex items-start">
                                    <i class="fas fa-check-circle text-blue-500 mt-1 mr-2 text-sm"></i>
                                    <span>使用哈希表统计元素出现次数</span>
                                </li>
                                <li class="flex items-start">
                                    <i class="fas fa-check-circle text-blue-500 mt-1 mr-2 text-sm"></i>
                                    <span>时间复杂度 O(n)，空间复杂度 O(n)</span>
                                </li>
                                <li class="flex items-start text-gray-500">
                                    <i class="fas fa-times-circle text-red-400 mt-1 mr-2 text-sm"></i>
                                    <span>需要额外的存储空间</span>
                                </li>
                            </ul>
                        </div>
                    </div>
                    <div class="w-full md:w-1/2 px-4">
                        <div class="bg-green-50 p-6 rounded-lg h-full">
                            <h3 class="text-xl font-semibold text-gray-800 mb-3 flex items-center">
                                <i class="fas fa-lightbulb text-green-500 mr-2"></i>优化解法
                            </h3>
                            <ul class="text-gray-700 space-y-2">
                                <li class="flex items-start">
                                    <i class="fas fa-check-circle text-green-500 mt-1 mr-2 text-sm"></i>
                                    <span>使用异或运算(XOR)巧妙解决</span>
                                </li>
                                <li class="flex items-start">
                                    <i class="fas fa-check-circle text-green-500 mt-1 mr-2 text-sm"></i>
                                    <span>时间复杂度 O(n)，空间复杂度 O(1)</span>
                                </li>
                                <li class="flex items-start">
                                    <i class="fas fa-check-circle text-green-500 mt-1 mr-2 text-sm"></i>
                                    <span>无需额外存储空间</span>
                                </li>
                            </ul>
                        </div>
                    </div>
                </div>
            </div>
        </section>

        <!-- XOR Properties -->
        <section id="concept" class="mb-16">
            <div class="bg-white rounded-xl shadow-md overflow-hidden">
                <div class="p-8">
                    <h2 class="text-3xl font-bold text-gray-800 mb-6 font-serif">
                        <i class="fas fa-atom text-indigo-500 mr-3"></i>异或运算的核心原理
                    </h2>
                    <p class="text-lg text-gray-700 mb-8 leading-relaxed">
                        异或运算(XOR)具有几个独特的数学性质，使其成为解决这个问题的完美工具：
                    </p>
                    
                    <div class="grid md:grid-cols-3 gap-6 mb-8">
                        <div class="property-card bg-white border border-gray-200 rounded-lg p-6 shadow-sm hover:shadow-md transition duration-300">
                            <div class="text-indigo-500 text-4xl mb-4">
                                <i class="fas fa-retweet"></i>
                            </div>
                            <h3 class="text-xl font-semibold text-gray-800 mb-2">自反性</h3>
                            <p class="text-gray-600">任何数与自身异或结果为0<br><code class="text-sm bg-gray-100 px-2 py-1 rounded">a ^ a = 0</code></p>
                        </div>
                        <div class="property-card bg-white border border-gray-200 rounded-lg p-6 shadow-sm hover:shadow-md transition duration-300">
                            <div class="text-indigo-500 text-4xl mb-4">
                                <i class="fas fa-dice-zero"></i>
                            </div>
                            <h3 class="text-xl font-semibold text-gray-800 mb-2">零性</h3>
                            <p class="text-gray-600">任何数与0异或结果为其自身<br><code class="text-sm bg-gray-100 px-2 py-1 rounded">a ^ 0 = a</code></p>
                        </div>
                        <div class="property-card bg-white border border-gray-200 rounded-lg p-6 shadow-sm hover:shadow-md transition duration-300">
                            <div class="text-indigo-500 text-4xl mb-4">
                                <i class="fas fa-random"></i>
                            </div>
                            <h3 class="text-xl font-semibold text-gray-800 mb-2">交换律和结合律</h3>
                            <p class="text-gray-600">运算顺序不影响最终结果<br><code class="text-sm bg-gray-100 px-2 py-1 rounded">a ^ b = b ^ a</code></p>
                        </div>
                    </div>

                    <div class="mb-8">
                        <h3 class="text-2xl font-semibold text-gray-800 mb-4 font-serif">原理可视化</h3>
                        <div class="mermaid">
                            graph LR
                                A[所有元素异或] --> B[成对元素抵消为0]
                                B --> C[最终结果就是唯一元素]
                        </div>
                    </div>

                    <div class="bg-blue-50 border-l-4 border-blue-500 p-4 rounded-r-lg mb-8">
                        <div class="flex">
                            <div class="flex-shrink-0">
                                <i class="fas fa-info-circle text-blue-500 text-xl mt-1 mr-3"></i>
                            </div>
                            <div>
                                <h4 class="text-lg font-semibold text-gray-800 mb-2">为什么这个方法有效？</h4>
                                <p class="text-gray-700">
                                    因为异或运算满足交换律和结合律，所有成对出现的元素会互相抵消为0，而0与唯一元素异或结果就是该元素本身。
                                </p>
                            </div>
                        </div>
                    </div>
                </div>
            </div>
        </section>

        <!-- Solution Section -->
        <section id="solution" class="mb-16">
            <div class="bg-white rounded-xl shadow-md overflow-hidden">
                <div class="p-8">
                    <h2 class="text-3xl font-bold text-gray-800 mb-6 font-serif">
                        <i class="fas fa-code text-indigo-500 mr-3"></i>解决方案
                    </h2>
                    
                    <div class="mb-8">
                        <h3 class="text-2xl font-semibold text-gray-800 mb-4 font-serif">算法步骤</h3>
                        <div class="relative">
                            <!-- Step 1 -->
                            <div class="flex items-start mb-8 step-item relative">
                                <div class="flex-shrink-0 bg-indigo-100 rounded-full step-icon flex items-center justify-center mr-4">
                                    <span class="text-indigo-600 font-bold text-xl">1</span>
                                </div>
                                <div class="flex-grow">
                                    <h4 class="text-lg font-semibold text-gray-800 mb-2">初始化变量</h4>
                                    <p class="text-gray-700">
                                        初始化一个变量 <code class="bg-gray-100 px-2 py-1 rounded">unique</code> 为 0
                                    </p>
                                </div>
                            </div>
                            
                            <!-- Step 2 -->
                            <div class="flex items-start mb-8 step-item relative">
                                <div class="flex-shrink-0 bg-indigo-100 rounded-full step-icon flex items-center justify-center mr-4">
                                    <span class="text-indigo-600 font-bold text-xl">2</span>
                                </div>
                                <div class="flex-grow">
                                    <h4 class="text-lg font-semibold text-gray-800 mb-2">遍历数组</h4>
                                    <p class="text-gray-700">
                                        对数组中的每个元素，与 <code class="bg-gray-100 px-2 py-1 rounded">unique</code> 进行异或操作
                                    </p>
                                </div>
                            </div>
                            
                            <!-- Step 3 -->
                            <div class="flex items-start step-item">
                                <div class="flex-shrink-0 bg-indigo-100 rounded-full step-icon flex items-center justify-center mr-4">
                                    <span class="text-indigo-600 font-bold text-xl">3</span>
                                </div>
                                <div class="flex-grow">
                                    <h4 class="text-lg font-semibold text-gray-800 mb-2">返回结果</h4>
                                    <p class="text-gray-700">
                                        遍历完成后，<code class="bg-gray-100 px-2 py-1 rounded">unique</code> 中保存的就是那个唯一出现的元素
                                    </p>
                                </div>
                            </div>
                        </div>
                    </div>

                    <div class="mb-8">
                        <h3 class="text-2xl font-semibold text-gray-800 mb-4 font-serif">代码实现</h3>
                        <div class="code-block p-4 mb-6">
                            <pre class="text-gray-200 text-sm md:text-base overflow-x-auto">
<code class="language-java">public class FindUniqueElementDemo {

    // 找到数组中唯一出现的元素
    public static int findUniqueElement(int[] nums) {
        int unique = 0;
        for (int num : nums) {
            unique ^= num; // 对所有元素进行异或
        }
        return unique; // 返回唯一出现的元素
    }

    public static void main(String[] args) {
        int[] nums = {1, 2, 3, 2, 1, 4, 4};
        int uniqueElement = findUniqueElement(nums);
        System.out.println("唯一出现的元素是: " + uniqueElement);
    }
}</code></pre>
                        </div>
                    </div>

                    <div class="mb-8">
                        <h3 class="text-2xl font-semibold text-gray-800 mb-4 font-serif">示例演示</h3>
                        <div class="bg-gray-50 p-6 rounded-lg">
                            <div class="mermaid">
                                flowchart LR
                                    A[数组: 1,2,3,2,1,4,4] --> B[0 ^ 1 = 1]
                                    B --> C[1 ^ 2 = 3]
                                    C --> D[3 ^ 3 = 0]
                                    D --> E[0 ^ 2 = 2]
                                    E --> F[2 ^ 1 = 3]
                                    F --> G[3 ^ 4 = 7]
                                    G --> H[7 ^ 4 = 3]
                                    H --> I[结果: 3]
                            </div>
                        </div>
                    </div>

                    <div class="bg-green-50 border-l-4 border-green-500 p-4 rounded-r-lg">
                        <div class="flex">
                            <div class="flex-shrink-0">
                                <i class="fas fa-check-circle text-green-500 text-xl mt-1 mr-3"></i>
                            </div>
                            <div>
                                <h4 class="text-lg font-semibold text-gray-800 mb-2">复杂度分析</h4>
                                <div class="grid md:grid-cols-2 gap-4">
                                    <div>
                                        <p class="font-medium text-gray-700">时间复杂度</p>
                                        <p class="text-gray-600">O(n) - 只需遍历一次数组</p>
                                    </div>
                                    <div>
                                        <p class="font-medium text-gray-700">空间复杂度</p>
                                        <p class="text-gray-600">O(1) - 只使用了一个额外变量</p>
                                    </div>
                                </div>
                            </div>
                        </div>
                    </div>
                </div>
            </div>
        </section>

        <!-- Applications Section -->
        <section class="mb-16">
            <div class="bg-white rounded-xl shadow-md overflow-hidden p-8">
                <h2 class="text-3xl font-bold text-gray-800 mb-6 font-serif">
                    <i class="fas fa-cubes text-indigo-500 mr-3"></i>应用场景
                </h2>
                <div class="grid md:grid-cols-2 gap-6">
                    <div class="bg-indigo-50 p-6 rounded-lg">
                        <h3 class="text-xl font-semibold text-gray-800 mb-3 flex items-center">
                            <i class="fas fa-memory text-indigo-500 mr-2"></i>内存敏感环境
                        </h3>
                        <p class="text-gray-700">
                            在嵌入式系统或内存受限的环境中，这种O(1)空间复杂度的算法特别有价值，因为它不需要额外的存储空间。
                        </p>
                    </div>
                    <div class="bg-purple-50 p-6 rounded-lg">
                        <h3 class="text-xl font-semibold text-gray-800 mb-3 flex items-center">
                            <i class="fas fa-bolt text-purple-500 mr-2"></i>性能关键系统
                        </h3>
                        <p class="text-gray-700">
                            对于需要高效处理大数据集的系统，这种线性时间复杂度的算法可以显著提高性能。
                        </p>
                    </div>
                </div>
            </div>
        </section>

        <!-- Summary Section -->
        <section class="mb-16">
            <div class="bg-gradient-to-r from-indigo-500 to-purple-600 rounded-xl shadow-md overflow-hidden p-8 text-white">
                <h2 class="text-3xl font-bold mb-6 font-serif">核心要点总结</h2>
                <ul class="space-y-4 text-lg">
                    <li class="flex items-start">
                        <i class="fas fa-check-circle mt-1 mr-3"></i>
                        <span>异或运算的自反性、零性和交换律是解决这个问题的关键</span>
                    </li>
                    <li class="flex items-start">
                        <i class="fas fa-check-circle mt-1 mr-3"></i>
                        <span>算法时间复杂度O(n)，空间复杂度O(1)，非常高效</span>
                    </li>
                    <li class="flex items-start">
                        <i class="fas fa-check-circle mt-1 mr-3"></i>
                        <span>适用于内存受限或性能关键的场景</span>
                    </li>
                    <li class="flex items-start">
                        <i class="fas fa-check-circle mt-1 mr-3"></i>
                        <span>是位运算在实际问题中应用的经典案例</span>
                    </li>
                </ul>
            </div>
        </section>
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